Gaël Monfils bent over at the waist, one hand on his knee and the other resting on the handle of his racket, which supported him like a cane as he tried to catch his breath inside a stifling Arthur Ashe Stadium.

For days the weather at the United States Open had been unusually cool and dry, but humidity rolled back in on Wednesday, testing the fortitude and resolve of the 33-year-old Monfils and his 23-year-old opponent, Matteo Berrettini, as they traded roundhouse punches for nearly four hours of exhausting tennis.

But the atmospheric conditions paled in comparison with the pressure that the two players built on their own through a captivating duel that did not end until the 24th-seeded Berrettini won the 324th point of the match.

It was the fourth time a man from Italy had advanced to the semifinal stage of a Grand Slam singles tournament in the Open Era.

On Friday, Berrettini will play No. 2 Rafael Nadal, who had to fight to beat No. 20 Diego Schwartzman, 6-4, 7-5, 6-2, in a match that was closer than the score indicated and ended at 12:39 a.m. With his rivals Novak Djokovic and Roger Federer out of the U.S. Open, Nadal is now the heavy favorite to win his 19th Grand Slam title.

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Rafael Nadal is in the U.S. Open semifinals for the eighth time.CreditMichelle V. Agins/The New York Times

The last male player from Italy to reach a U.S. Open semifinal was Corrado Barazzutti, who beat Brian Gottfried in a 1977 quarterfinal before losing to Jimmy Connors. Barazzutti, who captains the Italian Davis Cup and Fed Cup teams, sat in Berrettini’s box on Wednesday, cheering, worrying, fretting, gasping and agonizing along with everyone else who saw the match — or played in it.

“I was thinking, one of the best matches I ever saw,” Berrettini said in an on-court interview. “I was playing, but I was watching also.”

Berrettini is part of a new wave of Italian male players that includes Marco Cecchinato, who is ranked 66th in the world and made the semifinals of the French Open last year, and Lorenzo Sonego, No. 49. All of them are 26 or younger, and 11th-ranked Fabio Fognini, 32, is playing the best tennis of his career. Each is looking to become the first Italian man to win a Grand Slam singles title since Adriano Panatta won the French Open in 1976.

Right now Berrettini has the best chance, but he may have to rein in his nerves, which were on display when he double-faulted on his first match point — at 5-3, 40-30, of the fifth set. He failed to convert on three more match points, as Monfils kept reaching deep to extend the contest to its limit.

Finally, at 6-5 in the tiebreaker, Monfils hit a return long off a 125-mile-per-hour serve, and Berrettini collapsed on the court. He then jumped up and ran to the net to shake hands with Monfils, pounding his chest as he went.

Defeated players are not known to pound their chests, but Monfils would have been justified in doing so, considering how much heart he, too, showed in the match. Instead the Frenchman slapped Berrettini’s hand at the net, and the two competitors hugged in mutual appreciation.

“What a great fight,” Berrettini said. “I have to say congrats to Gaël.”

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“I gave my heart,” Monfils said after the defeat.CreditKarsten Moran for The New York Times

Monfils, a U.S. Open semifinalist in 2016, has drawn attention during the tournament this year not only for his tennis, but also for his relationship with Elina Svitolina, the fifth-seeded woman. The couple practice together and have discussed how each helps the other on court. Svitolina, who will play Serena Williams in a semifinal on Thursday, watched from Monfils’s box on Wednesday, knowing better than most what he was enduring in the match.

“I’m proud of myself, and I will be happy,” Monfils said. “I will be happy to cheer for my girlfriend tomorrow. Definitely if it can be one more day here.”

Berrettini said he did not remember any specific points, except the match winner. Then he held up one hand and put his thumb and forefinger together.

“I was a little bit tight,” he said, adding sarcastically, “but you didn’t see it, I guess.”

The match featured abrupt momentum swings, and Monfils showed remarkable determination just to stay in it. After he won the first set, fatigue seemed to set in, and he spent time bent over, seeking respite between serves.

Berrettini, a 6-foot-5 bruiser, won the second and third sets with relative ease and appeared to be headed for a four-set victory, as the older player’s exhaustion became more of a factor. But after the fourth set, the stadium roof was closed because of rain, a move that gave both players a chance to rest. They walked off court together during the break.

Berrettini seemed to be in command again in the fifth set, taking a 5-2 lead as the two parried and lunged at each other, shifting from offense to defense many times. Monfils held his serve to make it 5-3, and Berrettini got to his first match point.

His double fault was not even close, the second serve coming in slow and hitting the net. Somewhere in the back of his mind lurked the grim memory of the time six years ago that he blew 12 match points in a big junior tournament in Italy. That required three days to recover from, Berrettini said. This was not even half as bad.

But on the next point Monfils ripped a forehand winner crosscourt, and on break point, Berrettini hit a forehand into the net for an unforced error.

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“What a great fight,” Berrettini said after his win. “I have to say congrats to Gaël.”CreditKarsten Moran for The New York Times

Monfils held at 4-5, then looked to break back in the next game. At 15-0, Berrettini’s forehand hit the net tape and bounced onto Monfils’s side of the court. Monfils, who was at the baseline and headed into the right corner, skidded to stop, then ran in and put away a crosscourt approach-shot winner.

“I gave it all today,” said Monfils, who had 17 double faults. “I served bad, but I gave my heart.”

Then Berrettini scrambled back and held his serve. Now with Monfils trailing, 5-6, Berrettini had two more match points, which Monfils saved again, one with a tense, 17-shot rally. Monfils ultimately held his serve and sent the match to its only fitting conclusion: a tiebreaker.

It was not easy for Berrettini, of course, but at last his nerve held.

Rafael Nadal is the last of the Big Three standing.

While the other three men’s semifinalists — Matteo Berrettini, Grigor Dimitrov and Daniil Medvedev — are in the final four in the New York for the first time, Nadal reached his eighth U.S. Open semifinal, with a 6-4, 7-5, 6-2 victory over Diego Schwartzman.

The match lasted 2 hours 47 minutes in oppressive humidity. The second-seeded Nadal needed medical treatment on both his arms during the third set. Nadal rolled to a 4-0 lead, then Schwartzman won the next four games to get back on serve. But Nadal broke him at 4-5 to take the set.

Nadal broke Schwartzman twice to take a 5-1 lead in the second set, but then Schwartzman won four straight games again. With Schwartzman serving at 5-6, Nadal broke him for the third time in the set to take it, 7-5.

In the third set, Nadal built a 4-2 lead and did not let it go.

The Big Three of Nadal, Roger Federer and Novak Djokovic have won the last 11 men’s Grand Slam singles titles. Nadal is the only one left in the tournament who could extend the streak.

In U.S. Open debut, Bianca Andreescu is a semifinalist.

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Bianca Andreescu, 19, is the first teenager to reach the semifinals of the women’s tournament since Caroline Wozniacki in 2009. CreditMichelle V. Agins/The New York Times

Of course a shaky start didn’t bother 19-year-old Bianca Andreescu. She was brimming with confidence gained from not losing a completed match since March.

Despite a shoulder injury that sidelined her for months, Andreescu has soared from No. 152 to No. 15 in the rankings, and now she is in her first Grand Slam semifinal.

She defeated Elise Mertens, 3-6, 6-2, 6-3, on Wednesday night and will play Belinda Bencic in the semifinals on Thursday.

In her first U.S. Open, Andreescu, 19, is the first teenager to reach the semifinals of the women’s tournament since Caroline Wozniacki in 2009.

“Is this real life?” she said in her postmatch interview.

Before Wednesday night, Mertens had not lost a set at the tournament in singles or doubles, a discipline in which she has reached the semifinals alongside Aryna Sabalenka. Mertens had not even lost more than three games in a set through her first nine singles sets.

Belinda Bencic, at last, is in a major semifinal.

Belinda Bencic and Donna Vekic are about the same age. They are close friends and frequent practice partners. They were highly touted teenage players who, in their early 20s, were finally meeting late at a Grand Slam tournament.

So it was no surprise that for most of their United States Open quarterfinal on Wednesday, they were separated by only a few points.

But midway through the second set, the 13th-seeded Bencic pulled away to defeat the 23rd-seeded Vekic, 7-6 (5), 6-3, and advance to her first major semifinal.

Bencic, who beat No. 1 Naomi Osaka in the fourth round, is only 22. But in some ways her semifinal run is a long time coming.

She played her first Grand Slam quarterfinal in 2014 as a 17-year-old in her U.S. Open debut, and lost to Peng Shuai, 6-2, 6-1. She reached the top 10 at 18.

Bencic hadn’t been back to the final eight of a major since that 2014 Open, her career interrupted in 2017 because of wrist surgery.

Her ranking dropped outside the top 300 and she played low-level professional tournaments in Europe to work her way back. This season she has nine wins over top-10 players, the most on the WTA Tour. She will return to the top 10 next week.

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Belinda Bencic advanced to her first Grand Slam semifinal by defeating Donna Vekic. CreditKarsten Moran for The New York Times

When she was 17, Bencic said getting to the Open quarterfinals “was already very great. I don’t think that was a disappointment losing that.”

But this time she felt like she deserved to be in the semifinals.

“I felt really that I could take it, even though I was very nervous before the match,” she added.

After a tight first set, Bencic broke open the match after Vekic survived a long game, saving two break points, to hold for 3-2. Bencic won the next eight points to take a 4-3 lead and did not lose another game in the match. In the second set, she had only four unforced errors, three of which were double faults.

“I felt like I couldn’t get three good points together,” Vekic said. “I was, like, playing one point good, then bad. I don’t know. I didn’t really have a lot of rhythm out there today.”

On Thursday night, Bencic will play No. 15 Bianca Andreescu, who is also in her first major semifinal.

Bencic was as surprised as anyone that she is the last Swiss player left in singles. Her compatriots Roger Federer and Stan Wawrinka, who have 23 Grand Slam titles between them, lost their quarterfinal matches on Tuesday.

“This is not a good thing,” she said. “I’m not happy about this, actually. I’m kind of surprised, like I think everyone is. It would be really nice if the boys could also make it to semifinals. But I’m happy I can kind of do it for them.”

Jamie Murray closes in on a doubles double.

The schedule on Louis Armstrong Stadium on Wednesday featured six doubles matches, two of them with Jamie Murray of Britain. With his new men’s doubles partner, Neal Skupski, Murray defeated the American team of Jack Sock and Jackson Withrow, 4-6, 6-1, 7-6 (4). In the semifinals, Murray and Skupski will face the top-seeded team of Juan Sebastian Cabal and Robert Farah, who won Wimbledon in July.

A few hours later, Murray was back at Armstrong Stadium for the mixed doubles semifinal with Bethanie Mattek-Sands, and they beat Samantha Stosur and Rajeev Ram, 6-3, 6-1. Murray and Mattek-Sands are the defending champions at the U.S. Open; in Saturday’s final, they will play Michael Venus and Hao-Ching Chan.

Murray has won four Grand Slam titles in mixed doubles and two in men’s doubles.